Willingness to Pay for Clean Air: Evidence from Air Purifier Markets in China

Ito & Zhang

APEC 8990

Paper Presentations

September 19, 2024

Motivation

  • Air quality is poor in developing countries and has negative health and economic consequences
  • However, poor air quality may actually be optimal if WTP is low
  • Limited empirical evidence of WTP for clean air

Research Question

What is the willingness to pay for clean air?

Overview

  • Context: China 2006-2014
    • Developing country with poor air quality
  • Methods:
    • Spatial RDD based on Huai River heating policy
    • Product fixed effects and city fixed effects
    • Distance to plant IV to capture variation in transportation cost, which is a supply-side cost shifter
  • Findings:
    • Households have a high WTP for air quality, but heterogeneity exists by income and information

Data

China Cities 2006-2014

  1. Air purifier sales transaction data
    • ratio of HEPA purifier sales relative to non-HEPA purifier sales:
      • 1.2 for southern consumers compared to 2.0 for northern consumers
  2. City-level annual average PM10
  3. City-year measures on population, urban population, and GDP per capita
  4. Location data for cities
    • Distance to Huai River and factory or importing port locations of air purifiers

Demand for Air Purifiers

Random Utility Model

  • Consumer i in city c can purchase air purifier j at price p_{jc} to reduce indoor air pollution by x_{jc} = x_c \cdot e_j
  • Purifier j’s effectiveness at reducing indoor particulate matter e_j \in [0,1]
  • Observe markets for c = 1,...,C cities with i=1,...,I_c consumers

Then the conditional indirect utility of consumer i from purchasing air purifier j at city c is

u_{ijc} = \beta_i x_{jc} + \alpha_i \rho_{jc} + \eta_j + \lambda_c + \xi_{jc} + \epsilon_{ijc}

where x_{jc} represents the improvements in indoor air quality conditional on the purchase of product j, \rho_{jc} represents the price of product j in market c, \eta_j represents product fixed effects that capture utility gains from unobserved and observed product characteristics, \lambda_c represents city fixed effects, \xi_{jc} represents a product-city specific demand shock, and \epsilon_{ijc} represents a mean-zero stochastic term.

  • \beta_i: marginal utility for clean air
  • \alpha_i: marginal disutility of price

Demand for Air Purifiers

Logit Model

Assuming that \beta_i = \beta and \alpha_i = \alpha for consumer i and that the error term is distributed as a type I extreme value function, then consumer i purchases purifier j if u_{ijc} > u_{ikc} for \forall k \ne j. Then the market share for product j in city c is

s_{jc} = \frac{\exp \left( \beta x_{jc} + \alpha p_{jc} + \eta_j + \lambda_c + \xi_{jc} \right)}{\sum_{k=0}^{J} \exp \left( \beta x_{kc} + \alpha p_{kc} + \eta_k + \lambda_c + \xi_{kc} \right)}

which simplifies to

\begin{align*} s_{jc} &= \beta x_{jc} + \alpha \rho_{jc} + \eta_j + \lambda_c + \xi_{jc} \\ s_{jc} &= \beta x_{c} H_j + \alpha \rho_{jc} + \eta_j + \lambda_c + \xi_{jc} \end{align*}

  • x_{c}: ambient pollution
  • H_j: indicator variable for HEPA purifiers
  • Identifying variation: x_{c} H_j has city-by-product variation and \rho_{jc} has city-by-product

Empirical Strategy

RD

First Stage:

x_c = \gamma N_c + \phi_1 d_c + \phi_2 d_c N_c + \nu_l + \epsilon_c

where x_c represents PM10 in city c, N_c is the dummy variable for the north, d_c represents the distance between city c and the Huai River, and e_c is the error term.

  • \nu_l measures a discontinuous change in x_c at the Huai River border

Reduced form RD: \ln s_{jc} = \rho N_c H_j + \alpha p_{jc} + \left( \psi_1 d_c + \psi_2 d_c N_c + \nu_l \right) H_j + \eta_j + \lambda_c + \epsilon_{jc}

where s_{jc} and p_{jc} respectively represent the market share and the price of product j in city c, \eta_j represents product fixed effects, and \lambda_c represents city fixed effects.

Empirical Strategy

RD + IV

Estimate the MWTP for clean air (second stage):

\ln s_{jc} = \rho x_c H_j + \alpha p_{jc} + \left( \psi_1 d_c + \psi_2 d_c N_c + \nu_l \right) H_j + \eta_j + \lambda_c + \epsilon_{jc}

using N_c H_j as the instrument for x_c H_j

  • - \beta / \alpha represents the MWTP for one unit of PM10 (μg/m3)
  • Also uses transportation costs from a product’s manufacturing location to its market as an IV for price to capture a a supply-side cost shifter that does not directly affect demand
  • Exclusion restriction: the instruments must be uncorrelated with the error term given the control variables and fixed effects

Results

RD design at the Huai River boundary

Results

Standard Logit

Results

Standard Logit, Role of Information

Results

Marginal WTP for clean air and household income

Summary

  • MWTP for removing 1 μ g/m3 of PM10 per year is $1.34
    • Much higher for higher-income households
  • Implied value of a statistical life year (VSLY) per person is $455
    • Greater than Kremer et al. 2011 ($24) but less than León and Miguel 2017 ($13,500 Africans; $23,232 Non-Africans)
  • Drawbacks:
    • No information on other indoor avoidance behavior
    • Ignores dynamic decision making
    • Lack of analysis on market failures